Why radiodetection of UHECR still matters ?Lessons learned from the CODALEMA II & III experiments

+ Measurement of the primary particle energy+ Localization of the radio emitting sources

+ Towards the identification of the primary particle

Dr. Ahmed REBAIThursday, February 20, 2014

Das Karlsruher Institut für Technologie

Laboratoire de physique subatomique et des technologies associées Nantes

This work has been made a part under a grant from Region Pays de la Loire France and

CNRS/IN2P3 (Centre national de la recherche scientifique).

I would also like to thank Dr. Andreas Haungs and Dr. Tim Huege for the invitation

and Dr. Sabine Bucher for her administrative collaboration

1

Introduction

Recent Results in Ultra High Energy Cosmic Rays physics and their interpretation

Radiodetection of UHECR

The CODALEMA Experiment

●The measurement of the energy of the primary particle

Localization of the radio-emission source

2

Ultra High Energy Cosmic Rays puzzles

Many regions :- Low energies- Knees- ankle Many origins :- solar- galactic-extragalactic and ?Many techniques : Direct: satellites, balloons Indirect: ground base arrays (fluorescence,

particle detectors and antennas)

Open questions:Origin ? Nature ? Limit ?

Power law: Flux ~ E-2.7

Gaisser T. K. et al. Front. Phys. China. 8 (2013)

Transition ???

Knee

GZ

K o

r S

OM

ET

HIN

G E

LS

E?

3

Current results on the Ultra High Energy Cosmic Rays Physics

4

UHECR Origins

Question: How to reach 100 EeV (1020 eV)?

Cosmological origin (top-down mechanism) Massive particles decay (M.c2 ~ 1024

eV) Signature: photons/neutrinos Excluded by the Pierre Auger

Experiment (The Astrophysical Journal Letters, 755:L4 (7pp), 2012 August 10)

Astrophysic origin (bottom-up mechanism) Accélération de Fermi des particules chargées (Fermi: Phys. Rev. 75, 1169,

1949) => Limite ~ 1018 eV Proximité d'objets astrophysiques

=> Now, need to find sources

5

Sky maps @ Ep>55 EeV

UHECR sources

South hemisphere : Auger North hemisphere : TA/Hires

TA/Hires : directional correlation 44% (Astrophys.J. 757 (2012) 26)

Auger :increase of statistics and decrease of statistical correlation (61% to 33%)(Science 318 (2007) no. 5852, 938–943)

Propagation: effect of the Intergalactic magnetic fields?

6

UHECR propagation : GZK effect

During the 90s => disagreement between AGASA (Japan)-Hires1 (USA) experiments

2008: GZK cut confirmedby TA/Hires (Phys, Rev. Lett. 101 (2008) 061101) by Auger in 2010 (Phys. Lett. B 685 (2010) 239–246)

Interaction of UHECR with the Cosmic Microwave Background CMB

Auger

=>limit the observable universe at 100 Mpc=> depends on the primary nature=> @3.119 eV : Max energy of acceleration or propagation ?

7

UHECR Nature

Auger : Heavy composition favoured (Phys.Rev.Lett.104:091101,2010)

TA/Hires : lightening of the composition in function of the energy (Phys.Rev.Lett.104:161101,2010)

Xmax

: depth of the shower

maximum development => related to the nature of the primary

Difficulties on measurements and interpretations and strongly increasing cross-section

8

Proton interaction cross section @57TeV

(Phys.Rev.Lett. 109 (2012) 062002)

Constrained the hadronic models (QGSJET, Sibyll, Epos) used in particle physics

9

UHECR detection methodsParticle detection on the ground : Cerenkov detectors Scintillators

Detection of the fluorescence light

Advantages Disadvantages

Ground based detectors

Duty cycle near to 100% Dependence on hadronic modelsDeployed large surfaces > 1000 km2

Fluorescence telescopes

Low dependence on hadronic models Large volume detection

Low duty cycle near to 10%

10

Spectrum remains understood @UHEIll-defined chemical composition @UHEUnknown astrophysical origin @UHELow statistics at extreme energies

Radio-detection of Extensive Air Shower:A complementary detection method in evaluation11

13

γγ

ee e e

γ γee

Electromagnetic cascadePions cascadeNucleons cascade

γe γe γe

nπ°2n(Κ±π± ...hadrons)

Near shower axis Hadrons

π± desintegration

µ µ µµ

~90% of γ (>50 keV) ~9% electrons (>250 keV)~1% µ (>1 GeV) small hadron fraction

Sol

z First interaction

Xmax Nmax

Extensive Air Shower 12

Radio-detection of EAS

9% electrons/positrons

Radio emission mechanisms

Geomagnetic effect => deviation of electrons/positrons under the geomagnetic field effect => bipolar emission, transverse current, synchrotron emission => linear polarisation

Askaryan Negative charge-excess radiation => temporal variation of the negative charge excess => monopolar emission => radial field + Cherenkov-like coherence effect? (2010)

Forme du signal radio

Distanceshower-antenna

Radio signal shape

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Unipolar pulse models :

● REAS1, REAS2, ReAIRES

Bipolar pulse models:

● MGMR, REAS3, SELFAS2

Radio emission theoretical modelsComprehension of the radio signal => Intense theoretical efforts => several models available :

● Microscopic : use of CORSIKA and AIRES codes● Macroscopic : simplistic assumptions on the EAS phenomenology

+The total electric field

14

MHz radio-detection experiments

EASIER

16

AUGER

TREND

AERALOFAR

LOPES

15

CODALEMA experiment @Nançay• Radio-astronomy environment

• Electromagnetic quiet environment

• Far from big cities => Non-existence of strong transmitter

• But no possibility for end-to-end calibration.

~1 Km

~2 Km

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CODALEMA Actual SetupArray of 24 short antennas 21 polar. E-W

Array of 17 scintillatorExperiment TriggerEnergy Estimator Shower core locationArrival direction

Decametric array18 groups of 8 log-periodic phased antennas

30 self-triggered Antennas2 polar. (E-W + N-S) Objective : 60 on 1.5 km2

4 detector arrays

17

CODALEMA II : method of detection

Slave trigger mode

recording of the radio sky state

recording of the radio sky state

18

Radio transient selection

Recording radio waveforms in 0-200 MHz:Sampling frequency 1Gs / s on 2520 Points

19

Filtered radio transients

Event = 2 physical quantities/antenna (transient maximum amplitude and time of maximum transient )

Corrections :+Cables delays+Attenuation+Antennas gain

Digital filtering in the [20-83] MHz band

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Reconstruction of physical observables

Hypothesis : a plane wave front with equation :u.x+v.y+w.z+cte = 0(u,v,w) normal vector coordinates

Electric field profile

Arrivals direction : θ zenith angle ϕ azimuth angle

Allan model: exponential function with 4 parameters Ε = ε

0 exp(-d/d

0(x

c,y

c))

=> ε0 electric field on the shower axis

=> d0 radio shower lateral distance

=> (xc,y

c) shower core on the ground

Event = 2 physical quantities- Maximum amplitude of the transient- Time of maximum transient

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CODALEMA Results

CODALEMA model |vXB|EW

=>Est-West Polarisation of the electric field

=> Signal amplitude ~ |vXB|EW

D. Ardouin et al. Astro.ph 31 2009

Deficit of events near the magnetic axis

Evidence of a geomagnetic effect in the electric field generation mechanisms

22

B

The primary particle energy measurement with ε0 radio observable

+ A. Rebai et al. ArXiv:1210.1739, Oct. 2012 (submitted to Astro.Ph)+ ARENA2012, AIP Conf. Proc. 1535, 99-104 (2013)

ε0

Primary particle energy E

p

Correction factors:+ Geomagnetic emission?+ Askaryan charge-excess radiation?+ Cherenkov-like coherence effect?

23

Study of correlation between Ep and ε

0

E0 ~ Ep^alpha avec alpha ~ 1.0=> dépendance linéaire

Corrélation dépend :Erreurs sur EpErreurs sur e0

Fit function :

3 assumptions :* Linear-linear fit* Gaussian error * Independence relation between ε

0 and E

p

Goodness of fit study => Standard deviation of the distribution of E

p and E

0 residual

Existence of outlier events

σ(Ep)/E

p ~ 30%

σ(ε0)/ε

0 ~ 22% (Monte-Carlo)

(Only statistical errors No systematics for this study)

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1st correction factor : geomagnetic emissionGeomagnetic effect :

ε0 ~

E

p.|(vXB)

EW|

ε '0 ~

E

p.|(v'XB)

EW|

=> ε0 → ε

0 /|(vXB)

EW|

Overestimation of the energy of the events near to the geomagnetic axisBut no effect in E

p

=> The existence of a second contribution

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Additional mechanismAn simple assumption :Contribution proportional to the energy (i.e. total charge produced in the shower)

ε0 ~

E

p.|(vXB)

EW| + E

p.c

=> ε0 → ε

0 / ( |(vXB)

EW| + c )

0 < |(vXB)EW

| < 1

c > 0

Best resolution for |(vXB)EW

| close to 1 and c=0

=> Geomagnetic effect dominance

For small |(vXB)EW

| => improvement in

resolution when c increase => Ep.c dominates

70 events per window

Qu

alit

y cr

iter

ia

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Additional mechanism

Can we combine this new contribution to an existing electric field emission mechanism ?

Shower axis perpendicular component Shower axis parallel component

ε0 ~

E

p.|(vXB)

EW|+E

p.c.|sin(θ).sin(ϕ)|

Resolution degradation=> we reject the hypothesis

Interpretations with the current data set of 315 events:ε

0 ~

E

p.|(vXB)

EW|+E

p.c

1st term depends on the geomagnetic effect2nd term depends on the shower total charge => Askaryan charge-excess mechanism ?

ε0 ~

E

p.|(vXB)

EW|(1+c/|(vXB)

EW|+d/|(vXB)

EW|2+ ….)

Analogy with a magnetic field deflection created by a dipole => deflection of charged particles increases with |(vXB)

EW| => distance

between the particles increases => s there a limit imposed by the coherence of the emission??

27

Summary of the analysisOur interpretation with only 315 events :

ε0 ~

E

p.|(vXB)

EW| + E

p.c

1st term depends in the geomagnetic emission2nd term depends in the shower charge => Askaryan negative charge-excess mechanism ?

ε0 ~

E

p.|(vXB)

EW|.(1+c/|(vXB)

EW|)

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Energy resolution

Monte Carlo: Construction (E0, E

P)

distributions for fixed (∆E0, ∆E

P)

=> Construction of the abacus σ(EP-

E0)/E

P

=> σ(E

0) ~ 20%

=> Adopting a better parametrization RLDF (Gaussian)=> Improving the analysis chain + including systematic errors

Radio energy spectrum after calibrationRadio energy “Particle” energy

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Localization of radio emission sources➢ Motivations

➢ Experimental observations➢ Mathematical framework

➢ Ill-posedness formulation➢ Convex hull concept

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A. Rebai et al. arXiv:1208.3539+ ARENA2012, AIP Conf. Proc. 1535, 99-104 (2013)

Towards a self-radio trigger

In 3 years : 2030 eventsIn 4 days : 107 eventsAntenna trigger Antennas triggered by scintillators

Noise sources appearance

Objective : avoid to trigger the antenna array by another array

Transition from prototype experiments triggered by a particle detector arrays to self-triggered antenna arrays deployed on large surfaces

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Study of the radio interference (RFI)

Need to accurately locate interference sources to remove it => spherical emission assumption

Anthropogenic sources:Aircraft, power lines, transformers,electric motors ...Natural sources: Atmospheric storm discharges...

This is the crucial problem to be fixed in order to make radiodetection auto-triggering mode (radio trigger)!

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● The near field and far field are regions of the radio emission around the source

● Near field => spherical wavefront (airplanes, electric transformers …)

● Far field => planar wavefront (the sun during solar flare periods cf. J. Lamblin for the CODALEMA collab.. Radiodetection of astronomical phenomena in the cosmic ray dedicated CODALEMA experiment. In Proceeding of the 30th ICRC 2008)

Why a spherical wavefront hypothesis ?

source

Near field Far field

2*D2/λ

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Near to Lofar array

EDF electric transformer

Electric gate of a farm

RFI localization

►Correct localization expected for a spherical reconstruction:● immobile sources● Large number of detected events

+ Source/array position effect

►► localization problem ?

►►numerical simulation

CODALEMA III

TREND

AERA

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Model and simulation of the spherical waveTest array Spherical Propagation

1-Source at distance Rs

2- Arrival times distribution Computing

3-Introduction of errors

4-Generation of 1000 events

5-Reconstruction of the emission centre by minimizing an objective function with Simplex and Levenberg Marquardt (LVM) algorithms

35

Time resolution effect

Simplex algorithm: direct search (no gradient calculation)

Effect of temporal error :● σ

t=0 ns : good localization with a

statistical estimator● σ

t=3, 10 ns : Degradation of

reconstruction: spread of the Rs

distribution

σt=0 ns

σt=3 ns

σt=10 ns

Elongated distribution points : but θ, ϕ => good estimation !!!

36

LVM algorithm

Sensibility in initial conditions : Rini >> R

s => False results

Small modification in Rini => unpredictable results

=> Need to refine the analysis: apply other selection criteria

Initial conditions effect37

Simulation conclusions

When the temporal resolution increases: :

Reconstruction degradation=> distribution points spread

Bias appearance

==> Need for a detailed study of this spherical minimization

But the temporal resolution is not the only factor

● Source position relative to the array :✔ Source outside the array => bad reconstruction✗ Source inside the array => good reconstruction

Localization sensitive to the minimization algorithms (simplex and Levenberg-marquardt, linear search)

Initial conditions dependence

Multiple solutions (degeneration)

38

The followed approachThe minimization algorithms based on f descent direction search to reach the minimum (local or global) ● Solution = function minimum found● Global minimum => convex function => unicity of the

solution● Local minimum => non-convexe function=>

degeneration of the solution● Need to watch the first differential (minima)

and second (convexity)

Study the convexity of f:Jacobian and Hessian

● Coercivity of the objective function

● Sylvester criterion

● Ill-posed problem in the sense of Hadamard

● Ill-conditioned problem

Classification of the localization problem

in a more general framework

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Convexity of the objective function

Reasoning on the principal Hessian minor of order 4:

Sylvester Criterion : f is convex ⇔ All Hessian minors are positive

=> a negative minor => f is not convex => existence of several minimum

We choose

symbolic calculus:

With M is the Minkowski matrix

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Distribution of f minima

Search of minima:

=> Importance of the barycentre of the spatio-temporal variations of tagged antennas

Existence of a privileged direction of barycentre-source

● Importance of the closest antennas to the source

Analogy with the barycentre formula:

Difficulties in resolution => use of an empirical method

symbolic calculus:

=>

41

1D array case3 hypothesis :● Source inside the array● Source outside the array● Source outside the array but off-line

Source interne

Particular role for the segment => convex hullRole of the nearest antenna to the source

Source externe

42

1D array case (external source)

Source outside the segment and off-line

Constraints => light cones

Unconstrained Minimization results => Solutions lie on a half-line

43

2D array case (internal source)

Convex hull role

Real case : source inside the antenna array

44

2D array case (external source)

Presence of local minima Distribution on a line

Role of the convex hull

Existence of privileged half-line

Real case : source on the ground and outside the array convex hull (RFI sources)

45

2D array case : source in the sky

Good estimation of the arrivals direction

source

Antenna array on the ground

46

Ill-conditioned problem47Condition number : measure how sensitive a function is to changes or errors in the input

κ(H)=||H-1||*||H|| ~ λmax

(H)/λmin

(H) (eignevalues of H)

(F. Delprat-Jannaud and P. Lailly, Ill-Posed and Well-Posed Formulation of the Reflection Travel Time Tomography Problem, J. of Geophysical Research, vol. 98, No. B4, p. 6589, April 10, 1993.)

Low condition number (~1) => well-conditioned problem

High condition number (>>1) => ill-conditioned problem

Classification of the localization problem

(1902) A physics problem is ill-posed if:1 – no solution

or2 – has many solutions

or3 – the solution has a strong dependence

In the different parameters of the problem (initial conditions, boundary conditions, data errors)

(2) et (3) => localization problem is ill-posed in the case of a source external to the tagged antenna convex hull

localization problem is well posed in the case of an internal source to the convex hull of antenna

Jacque Hadamard

48

Best method to circumvent the problem is not yet found

R(estimated)=4000 m R(estimated)=9700 m

Direct search attempt

1 - Quantification of the phase space in a cubic grid: step ~ 50 m in space, time step ~ 10 ns

2 - Using the planar fit to determine the search directions in the phase space

3 - Calculate the value of f on a grid

4 - Search absolute minimum

49

Best method to circumvent the problem is not yet found

Direct search attempt

But in the case of a source in the sky => Bias

50

Source on the ground

PhD of Diego Torres

And now EAS ?

Observation of a time shift relative to the plane wavefront assumption

But only one realization per event ► Problem for a statistical estimation of the source position

Hypothesis : the signal maximum amplitude linkedTo the development region of the shower (X

max ?)

51Dimensions of the charged particles pancake:+ Longitudinal spreading ~ few meters (J. Linsley, "Thickness of the particle swarm in cosmic-ray air showers," Journal Phys G vol. 12, No. 1., P. 51, 1986)+ Lateral spreading: limited by the effect of coherence => band [23-83] MHz => ~ 3 - ~ 13 m

Apparent point source localized in space => spherical emission

Data

3D detectors in the water and in the iceVolume detector array (not a new idea) : Askaryan during the 70s and DUMAND array during 90s.

Slide from ARENA 2010 presentation “H. Ralf”

52

3D detectors in the water and the ice53

Exposure of high altitude antennas (mountains, ballons, satellite) P. Motloch, N. Hollon, P. Privitera, On the prospects of ultra-high energy cosmic rays detection by high altitude antennas (arXiv:1309.0561) accepted in Astro. Part.

3D convex hull: Towards 3D antenna array

Our idea

A. Rebai and Ramzi Boussaid Formulation of the emission sources localization problem in the case

of a selftriggered radio-detection experiment: Between Ill-posedness and Regularization (to be submitted)

Anita

Forte satellite

54

55

Conclusions

+ Energy analysis was improved

indication of the presence of several radio emission mechanisms

Estimation of the energy resolution of ~ 20%

+ Prespective: More accurate LDF (Gaussian) => resolution enhancement

+ RFI observations and simulations => difficulties in interpretations

Study the objective function

Role of the convex hull

Role of the half-line that binds the antennas barycentre and the source

We need to work with mathematicians (multidisciplinary approach)

56